If \(2^{2x - 3y} = 32\) and \(\log_{y} x = 2\), find the values of x and y.

If (x + 2) and (x - 1) are factors of \(f(x) = 6x^{4} + mx^{3} - 13x^{2} + nx + 14\), find the 

(a) values of m and n.

(b) remainder when f(x) is divided be (x + 1).

Find the equation of the tangent to the curve \(y = \frac{x - 1}{2x + 1}, x \neq -\frac{1}{2}\) at the point (1, 0).

(a) There are 6 points in a plane. How many triangles can be formed with the points?

(b) A family of 6 is to be seated in a row . In how many ways can this be done if the father and mother are not to be seated together?

The table shows the distribution of the ages of a group of people in a village.

Using an assumed mean of 24.5, calculate the mean of the distribution.